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1 /*
2  * Mesa 3-D graphics library
3  *
4  * Copyright (C) 1999-2007  Brian Paul   All Rights Reserved.
5  * Copyright 2015 Philip Taylor <philip@zaynar.co.uk>
6  * Copyright 2018 Advanced Micro Devices, Inc.
7  * Copyright (C) 2018-2019 Intel Corporation
8  *
9  * Permission is hereby granted, free of charge, to any person obtaining a
10  * copy of this software and associated documentation files (the "Software"),
11  * to deal in the Software without restriction, including without limitation
12  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
13  * and/or sell copies of the Software, and to permit persons to whom the
14  * Software is furnished to do so, subject to the following conditions:
15  *
16  * The above copyright notice and this permission notice shall be included
17  * in all copies or substantial portions of the Software.
18  *
19  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
20  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
21  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
22  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
23  * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
24  * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
25  * OTHER DEALINGS IN THE SOFTWARE.
26  */
27 
28 #include <math.h>
29 #include <assert.h>
30 #include "half_float.h"
31 #include "rounding.h"
32 #include "softfloat.h"
33 #include "macros.h"
34 #include "u_math.h"
35 
36 typedef union { float f; int32_t i; uint32_t u; } fi_type;
37 
38 /**
39  * Convert a 4-byte float to a 2-byte half float.
40  *
41  * Not all float32 values can be represented exactly as a float16 value. We
42  * round such intermediate float32 values to the nearest float16. When the
43  * float32 lies exactly between to float16 values, we round to the one with
44  * an even mantissa.
45  *
46  * This rounding behavior has several benefits:
47  *   - It has no sign bias.
48  *
49  *   - It reproduces the behavior of real hardware: opcode F32TO16 in Intel's
50  *     GPU ISA.
51  *
52  *   - By reproducing the behavior of the GPU (at least on Intel hardware),
53  *     compile-time evaluation of constant packHalf2x16 GLSL expressions will
54  *     result in the same value as if the expression were executed on the GPU.
55  */
56 uint16_t
_mesa_float_to_half_slow(float val)57 _mesa_float_to_half_slow(float val)
58 {
59    const fi_type fi = {val};
60    const int flt_m = fi.i & 0x7fffff;
61    const int flt_e = (fi.i >> 23) & 0xff;
62    const int flt_s = (fi.i >> 31) & 0x1;
63    int s, e, m = 0;
64    uint16_t result;
65 
66    /* sign bit */
67    s = flt_s;
68 
69    /* handle special cases */
70    if ((flt_e == 0) && (flt_m == 0)) {
71       /* zero */
72       /* m = 0; - already set */
73       e = 0;
74    }
75    else if ((flt_e == 0) && (flt_m != 0)) {
76       /* denorm -- denorm float maps to 0 half */
77       /* m = 0; - already set */
78       e = 0;
79    }
80    else if ((flt_e == 0xff) && (flt_m == 0)) {
81       /* infinity */
82       /* m = 0; - already set */
83       e = 31;
84    }
85    else if ((flt_e == 0xff) && (flt_m != 0)) {
86       /* NaN */
87       m = 1;
88       e = 31;
89    }
90    else {
91       /* regular number */
92       const int new_exp = flt_e - 127;
93       if (new_exp < -14) {
94          /* The float32 lies in the range (0.0, min_normal16) and is rounded
95           * to a nearby float16 value. The result will be either zero, subnormal,
96           * or normal.
97           */
98          e = 0;
99          m = _mesa_lroundevenf((1 << 24) * fabsf(fi.f));
100       }
101       else if (new_exp > 15) {
102          /* map this value to infinity */
103          /* m = 0; - already set */
104          e = 31;
105       }
106       else {
107          /* The float32 lies in the range
108           *   [min_normal16, max_normal16 + max_step16)
109           * and is rounded to a nearby float16 value. The result will be
110           * either normal or infinite.
111           */
112          e = new_exp + 15;
113          m = _mesa_lroundevenf(flt_m / (float) (1 << 13));
114       }
115    }
116 
117    assert(0 <= m && m <= 1024);
118    if (m == 1024) {
119       /* The float32 was rounded upwards into the range of the next exponent,
120        * so bump the exponent. This correctly handles the case where f32
121        * should be rounded up to float16 infinity.
122        */
123       ++e;
124       m = 0;
125    }
126 
127    result = (s << 15) | (e << 10) | m;
128    return result;
129 }
130 
131 uint16_t
_mesa_float_to_float16_rtz_slow(float val)132 _mesa_float_to_float16_rtz_slow(float val)
133 {
134     return _mesa_float_to_half_rtz_slow(val);
135 }
136 
137 /**
138  * Convert a 2-byte half float to a 4-byte float.
139  * Based on code from:
140  * http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html
141  */
142 float
_mesa_half_to_float_slow(uint16_t val)143 _mesa_half_to_float_slow(uint16_t val)
144 {
145    union fi infnan;
146    union fi magic;
147    union fi f32;
148 
149    infnan.ui = 0x8f << 23;
150    infnan.f = 65536.0f;
151    magic.ui  = 0xef << 23;
152 
153    /* Exponent / Mantissa */
154    f32.ui = (val & 0x7fff) << 13;
155 
156    /* Adjust */
157    f32.f *= magic.f;
158    /* XXX: The magic mul relies on denorms being available */
159 
160    /* Inf / NaN */
161    if (f32.f >= infnan.f)
162       f32.ui |= 0xff << 23;
163 
164    /* Sign */
165    f32.ui |= (uint32_t)(val & 0x8000) << 16;
166 
167    return f32.f;
168 }
169 
170 /**
171   * Convert 0.0 to 0x00, 1.0 to 0xff.
172   * Values outside the range [0.0, 1.0] will give undefined results.
173   */
_mesa_half_to_unorm8(uint16_t val)174 uint8_t _mesa_half_to_unorm8(uint16_t val)
175 {
176    const int m = val & 0x3ff;
177    const int e = (val >> 10) & 0x1f;
178    ASSERTED const int s = (val >> 15) & 0x1;
179 
180    /* v = round_to_nearest(1.mmmmmmmmmm * 2^(e-15) * 255)
181     *   = round_to_nearest((1.mmmmmmmmmm * 255) * 2^(e-15))
182     *   = round_to_nearest((1mmmmmmmmmm * 255) * 2^(e-25))
183     *   = round_to_zero((1mmmmmmmmmm * 255) * 2^(e-25) + 0.5)
184     *   = round_to_zero(((1mmmmmmmmmm * 255) * 2^(e-24) + 1) / 2)
185     *
186     * This happens to give the correct answer for zero/subnormals too
187     */
188    assert(s == 0 && val <= FP16_ONE); /* check 0 <= this <= 1 */
189    /* (implies e <= 15, which means the bit-shifts below are safe) */
190 
191    uint32_t v = ((1 << 10) | m) * 255;
192    v = ((v >> (24 - e)) + 1) >> 1;
193    return v;
194 }
195 
196 /**
197   * Takes a uint16_t, divides by 65536, converts the infinite-precision
198   * result to fp16 with round-to-zero. Used by the ASTC decoder.
199   */
_mesa_uint16_div_64k_to_half(uint16_t v)200 uint16_t _mesa_uint16_div_64k_to_half(uint16_t v)
201 {
202    /* Zero or subnormal. Set the mantissa to (v << 8) and return. */
203    if (v < 4)
204       return v << 8;
205 
206    /* Count the leading 0s in the uint16_t */
207 #ifdef HAVE___BUILTIN_CLZ
208    int n = __builtin_clz(v) - 16;
209 #else
210    int n = 16;
211    for (int i = 15; i >= 0; i--) {
212       if (v & (1 << i)) {
213          n = 15 - i;
214          break;
215       }
216    }
217 #endif
218 
219    /* Shift the mantissa up so bit 16 is the hidden 1 bit,
220     * mask it off, then shift back down to 10 bits
221     */
222    int m = ( ((uint32_t)v << (n + 1)) & 0xffff ) >> 6;
223 
224    /*  (0{n} 1 X{15-n}) * 2^-16
225     * = 1.X * 2^(15-n-16)
226     * = 1.X * 2^(14-n - 15)
227     * which is the FP16 form with e = 14 - n
228     */
229    int e = 14 - n;
230 
231    assert(e >= 1 && e <= 30);
232    assert(m >= 0 && m < 0x400);
233 
234    return (e << 10) | m;
235 }
236